DOI QR코드

DOI QR Code

Time Series Perturbation Modeling Algorithm : Combination of Genetic Programming and Quantum Mechanical Perturbation Theory

시계열 섭동 모델링 알고리즘 : 운전자 프로그래밍과 양자역학 섭동이론의 통합

  • Lee, Geum-Yong (Dept.of Information Communication Engineering, Youngsan University)
  • 이금용 (영산대학교 정보통신공학부)
  • Published : 2002.06.01

Abstract

Genetic programming (GP) has been combined with quantum mechanical perturbation theory to make a new algorithm to construct mathematical models and perform predictions for chaotic time series from real world. Procedural similarities between time series modeling and perturbation theory to solve quantum mechanical wave equations are discussed, and the exemplary GP approach for implementing them is proposed. The approach is based on multiple populations and uses orthogonal functions for GP function set. GP is applied to original time series to get the first mathematical model. Numerical values of the model are subtracted from the original time series data to form a residual time series which is again subject to GP modeling procedure. The process is repeated until predetermined terminating conditions are met. The algorithm has been successfully applied to construct highly effective mathematical models for many real world chaotic time series. Comparisons with other methodologies and topics for further study are also introduced.

양자역학 섭동이론과 유전자프로그래밍(GP) 기법을 접목시킴으로써 실세계(Real-world)에서 발생하는 카오스 시계열에 대하여 수학모델을 구축, 예측하기 위한 새로운 알고리즘을 개발하였다. 시계열 분석과 양자역학 파동방정식의 해를 구하는 섭동이론과의 절차적 유사성을 논하고, 이것을 GP로 구현하는 전형적 접근방안을 제시한다. 함수집합(Function Set)으로서 직교함수(Orthogonal Functions)를 이용하고 병렬 집단을 사용하는 GP를 이용하여 원 시계열에 대한 초기 수학모델을 구하고, 원 시계열 데이터로부터 모델의 평가값을 뺀 나머지로 구성되는 잔여 시계열에 대하여 다시 GP를 적용하는 과정을 일정한 종료조건이 충족될 때가지 반복함으로써 실세계 카오스 시계열에 대한 정확성 높은 수학모델을 구축하는데 성공하였다. 타 방법론과의 비교와 향후 해결과제에 대하여도 소개한다.

Keywords

References

  1. Weigend, A.S. and Gershenfeld, N.A., Eds., 'Time Series Prediction Forecasting the future and Understanding the Past,' SFI Studies in the Science of Complexity, Vol.XV, Addison Wesley Publishing Co., 1993
  2. Box, G.E.P., Jenkins, G.M. and Reinsel, G.C., 'Time Series Analysis,' 3rd Ed., Englewood Cliffs, NJ : Prentice Hall, 1994
  3. Ivakhnenko, A.G., 'Polynomial Theory of Complex Systems,' IEEE Trans. Syst. Man Cybern., Vol.1(4), pp.364-378, 1971 https://doi.org/10.1109/TSMC.1971.4308320
  4. Koza, J.R., 'Genetic Programming II,' MIT Press, 1994
  5. Oakeley, H., 'Two Scientific Application of Genetic Programming : Stack Filters and Non-Linear Equation Fitting to Chaotic Data,' Advances in Genetic Programming, K.E.Kinnear Jr., Eds., MIT Press, pp.369-389, 1994
  6. Iba, H., de Garis, H. and Sato, T., 'Genetic Programming using a Minimum Description Length Principle,' Advances in Genetic Programming, K.E. Kinnear Jr. Eds., MIT Press, pp.265-284, 1994
  7. Rae, A.I.M., 'Quantum Mechanics,' 3rd Ed., University of Birmingham, UK, IOP Publishing Ltd., 1992
  8. Nayeh, A.H., 'Introduction to Perturbation Techniques,' John Wiley & Sons, 1993
  9. Geman, S. et al., 'Neural Networks and the Bias/Variance Dilemma,' Neural Computation, Vol.4, pp.1-58, 1992 https://doi.org/10.1162/neco.1992.4.1.1
  10. Luke, S., and L. Spector, 'Evolving Teamwork and Coordination with Genetic Programming,' Genetic Programming 1996 : Proceedings of the First Annual Conference, MIT Press, pp.150-156, 1996
  11. Guy L. Steele, 'Common Lisp,' 2nd Edition, 1991
  12. Sansone, G., Sansome, G. and Diamond, A.H., 'Orthogonal Functions,' Dover Publications, 1991
  13. Casdagli, M.C., 'Nonlinear prediction of chaotic time series,' Physics D.35, pp.335-356, 1989 https://doi.org/10.1016/0167-2789(89)90074-2
  14. Geumyong, Lee, 'Genetic Recursive Regression for modeling and forecasting real-world chaotic time series,' Advances in Genetic Programming, Vol.3, Chapter 17, MIT Press, 1999
  15. Kreider, J.F., 'results.asc,' ASHRAE Competition ftp site, ftp.cs.colorado.edu/pub/energy-shootout, 1993
  16. Smith, L.A., 'Does a meeting in Santa Fe imply chaos?,' Time Series Prediction Forecasting the Future and Understanding the Past, A.S. Weigend, and N.A. Gershenfeld, Eds., SFI Studies in the Science of Complexity, Addison Wesley Publishing Co., Vol.XV, pp.323-343, 1993
  17. Kailath, T., Linear Systems, Englewood Cliffs, NJ : Prentice Hall, 1980
  18. Dechert, W.D., 'Chaos Theory in Economics : Methods, Models and Evidence,' International Library of Critical Writings in Economics, Edward Elgar Pub., No.66, 1996
  19. Geumyong, Lee, 'Modeling and Forecasting Major US Economic Time Series Based on Intelligent Symbolic Processing Technology,' 영산대학교 출판사, 영산논총, 제4집, pp.220-226, Aug., 1999